Write the linear equation that gives the rule for this table. Write your answer as an equation with y first, followed by an equals sign.
Understand the Problem
The question asks to determine the equation that gives the rule for the table, we need to work our way backwards and determine the slope and the intersect. The answer should be provided as 'y = ...'
Answer
$y = x + 88$
Answer for screen readers
$y = x + 88$
Steps to Solve
- Calculate the slope
To calculate the slope, we can use the formula:
$slope = \frac{y_2 - y_1}{x_2 - x_1}$
Using the points (1, 89) and (2, 90) from the table:
$slope = \frac{90 - 89}{2 - 1} = \frac{1}{1} = 1$
- Determine the y-intercept
The slope-intercept form of a linear equation is given by:
$y = mx + b$
where $m$ is the slope and $b$ is the y-intercept. We already have the slope $m = 1$. Now we can plug in one of the points from the table into the equation to solve for $b$. Let's use the point (1, 89):
$89 = (1)(1) + b$
$89 = 1 + b$
$b = 89 - 1 = 88$
- Write the linear equation
Now that we have the slope $m = 1$ and the y-intercept $b = 88$, we can write the linear equation as: $y = 1x + 88$
Which simplifies to: $y = x + 88$
$y = x + 88$
More Information
The equation $y = x + 88$ represents the linear relationship described in the table. For every unit increase in $x$, $y$ increases by one, starting from $y = 89$ when $x = 1$.
Tips
A common mistake is to miscalculate the slope or y-intercept. Always double-check your calculations, especially when subtracting negative numbers. Another mistake is to confuse the x and y values when calculating the slope.
AI-generated content may contain errors. Please verify critical information
